Question

1) A claim is made that employees work less than 15 hours/week, on average, at "Joe's Pretty-Good Burgers".

• What kind of hypotheisis test is this?
  • 2 Proportions z-test
  • 1 Proportion z-test
  • 2 Independent Means t-test
  • 2 Means Matched Pairs t-test
  • 1 Mean t-test

• • 2) Which hypotheses do we want to test?
• H₀: μ₁ = 15
  H_A: μ₁ > 15
• H₀: μ₁ ≠ 15
  H_A: μ₁ = 15
• H₀: μ₁ = 15
  H_A: μ₁ ≠ 15
• H₀: μ₁ = 15
  H_A: μ₁ < 15

Answer 1

1) Here, We are testing the claim about the mean Working hours of the employees that whether this mean is less than 15 hours per week (a specified value) or not. So, we will take sample of working hours of employees and find it's mean and standard deviation. Hence it is testing of mean and not proportion.

Since we have single mean and we are comparing it with a specified value, it is testing of single mean and not two means.

Also the population standard deviation is unknown, hence, we can not use z test. So, we will have to use t-test.

Hence, the appropriate test will be one mean t-test.

2) Hypothesis can be framed as -

Null hypothesis : The mean working hours of employees is 15 hours per week.

Alternative hypothesis: The mean working hours of employees is less than 15 hours per week.